Well the Bible would be left in the room of the athlete yes? Or perhaps in their gear bag at the side of the track? Its not like anybody will start holding a Bible over their head after winning. What religious articles, athletes have in their possession, should be the athletes own personal business, not that of authorities in Beijing, as long as they are not attempting to make a forceful public statement with it.
I can't say there was any Olympics, at least in my memory, that involved athletes doing anything involving religious articles, which could be regarded as controversial. Why this sudden concern in Beijing? Are they worried about their own Muslim population and their reactions?
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